/*
 * @lc app=leetcode.cn id=64 lang=cpp
 *
 * [64] 最小路径和
 */
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <cmath>

using namespace std;
// @lc code=start
class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> dp(m,vector<int> (n));
        //dp初始化
        dp[0][0] = grid[0][0];
        for(int i = 1;i < n;i++) {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }
        for(int i = 1;i < m;i++) {
            dp[i][0] = dp[i-1][0] + grid[i][0];
        }
        //遍历递推
        for(int i = 1;i < m;i++) {
            for(int j = 1;j < n;j++) {
                dp[i][j] = min(dp[i-1][j] ,dp[i][j-1])+grid[i][j];
            }
        }
        return dp[m-1][n-1];
    }
};
// @lc code=end

